Rotten Tomatoes

Launched in August 1998 by Senh Duong, Rotten Tomatoes is an American review aggregation website for film and television.

IMDB

Univariate Analysis of Categorical Variables

The purpose of the univariate analysis of categorical variables was to examine the relative frequencies and proportions of observations for each level of the categorical level. The categorical variables included at this stage of the analysis are indicated in Table 3.

For brevity reasons, this section briefly covers the five variables most important to the modeling effort, in priority order. The complete analysis can be found in Appendix B.

Univariate Analysis of Quantitative Variables

The primary aim of this analysis was to examine the distribution of the variables vis-a-vis a normal distribution, and to identify potential outliers. Summary statistics, histograms, boxplots, normal quantile-quantile plots were rendered for each variable. The quantitative variables included at this stage of the analysis are indicated in Table 4.

Again, the five most influential quantitative variables are covered here in some detail. The complete analysis can be found in Appendix B.

NULL

Dependent Variable

As mentioned above, the first objective was to identify an available variable that would proxy for box office success. Correlation tests were conducted between the quantitative variables and the log of box office revenue. The top 5 variables most highly correlated with log of box office revenue are summarized in Table 20.

Figure 35: Scatterplots of variables most highly correlated with log of box office revenue

The scatter plots in Figure 35, confirmed it. The log of the number of IMDB votes would proxy for box office revenue and correlation with this dependent variable was the focus of the bivariate analysis that follows.

Categorical Variable Analysis

Association tests were conducted between the categorical variables and the log number of IMDB votes and Table 21 summarizes the most highly associated variables.

As expected, director and studio were highly associated with film popularity.

Quantitative Variable Analysis

The correlations between the quantitative variables and the log number of IMDB votes are listed in Table 22 in order of highest to lowest correlation.

The log of cast votes was highly correlated with the log number of IMDB votes; whereas cast experience was significantly less correlated. Surprisingly, the number of days between the dvd release and the theatrical release was negatively correlated with IMDB votes, causing one to consider the proportion of IMDB votes cast by DVD viewers.

Forward Selection

The forward selection process begins with a null model then all variables are added to the model, one-by-one, and the model that provides the greatest improvement in adjusted R-squared is selected. If the adjusted R-squared for this set was greater than the best R-squared for the model, it was selected. The process repeats until all predictors were evaluated. Table 24 provides the the forward selection process and the summary statistics for each step.

Table 24 Forward Selection Process

Best Director / Actor / Actress

As indicated in Figure 36, the percentages of films with best director, actor and actress oscars were 7%, 15%, and 12%, respectively. Again, the decision in this case was to assume that with random sampling, these ratios reflected the true population proportions, and to keep the variables for further analysis during the modeling stage.

Figure 36: Best director/actor/actress

Best Picture

Since the proportion of films nominated for and winning best picture were so small, this variable was not likely to be a good predictor of movie popularity. The bivariate analysis below will illuminate this further.

Figure 37: Best picture nominations and wins

Genre

The drama genre represented a plurality of the releases in the sample, followed by comedy action & adventure then mystery & suspense. The top four genres account for nearly 80% of the films in the sample. Figure 38: Films by genre

MPAA Rating

Rated R films accounted for over 0% of the releases, followed by PG and PG-13. Collectively, R, PG, and PG-13 rated films represent 90% of the films in the sample. NC-17 films were excluded from this analysis. Figure 39: Films by MPAA Rating

Month of Theatrical Release

Though the plurality of features in the sample (32%) were released during the months of January, June, October and December, the distribution of theatrical release months appeared fairly balanced within the sample. Figure 40: Theatrical releases by month

Season of Theatrical Release

The plurality of features in the sample were released during the fall and summer months with over 20% opening in the month of December alone. Figure 41: Theatrical releases by season

Audience Scores

This variable captured the audience scores from Rotten Tomatoes for each film

Figure 42: Audience score histogram and QQ Plot

Figure 43: Audience score boxplot

Central Tendency: The summary statistics (Table 27) the central tendency for audience score was 61 points and 57.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.37, corresponds with a coefficient of variation of 49.4%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.26), indicated that the distribution of audience score was approximately symmetric. The sample kurtosis (-1.17), indicated that the distribution of audience score was platykurtic or light-tailed. The histogram and QQ plot in Figure 42 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 43, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 83, and 50, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 158]. Indeed, this confirmed the existence of no outliers.

Box Office

Total lifetime box office revenue was obtained for a subset of 100 randomly selected films from the movie data set. This is an analysis of box office revenue for this random sampling.

Figure 44: Box office revenue histogram and QQ Plot

Figure 45: Box office revenue boxplot

Central Tendency: The summary statistics (Table 28) the central tendency for box office was 13,349,927 dollars and 38,611,879.9 dollars for the median and mean, respectively.

Dispersion: The standard deviation, s = 68,922,520.54, corresponds with a coefficient of variation of 178.5%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.55), indicated that the distribution of box office was right-skewed. The sample kurtosis (31.2), indicated that the distribution of box office was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 44 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 45, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1,064,483, 49,655,390, and 48,590,907, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 122,541,750.5]. Indeed, this confirmed the existence of 21 outliers.

Log Box Office

This is a log transformation of the box office variable.

Figure 46: Log box office revenue histogram and QQ Plot

Figure 47: Log box office revenue boxplot

Central Tendency: The summary statistics (Table 29) the central tendency for log box office was 23.7 log(dollars) and 22.6 log(dollars) for the median and mean, respectively.

Dispersion: The standard deviation, s = 3.84, corresponds with a coefficient of variation of 17%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.8), indicated that the distribution of log box office was left-skewed. The sample kurtosis (-0.21), indicated that the distribution of log box office was platykurtic or light-tailed. The histogram and QQ plot in Figure 46 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 47, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 20, 25.6, and 5.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [11.75, 33.85]. Indeed, this confirmed the existence of 1 outliers.

Cast Experience

This derived variable measured the relative experience of a given cast and was defined as the sum of the observations for the cast associated with each film.

Figure 48: Cast experience histogram and QQ Plot

Figure 49: Cast experience boxplot

Central Tendency: The summary statistics (Table 30) the central tendency for cast experience was 7 films and 7.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.16, corresponds with a coefficient of variation of 29%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (0.89), indicated that the distribution of cast experience was right-skewed. The sample kurtosis (0.32), indicated that the distribution of cast experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 48 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 49, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 6, 9, and 3, respectively. This yielded a 1.5xIQR ‘acceptable’ range [1.5, 13.5]. Indeed, this confirmed the existence of 7 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Log Cast Experience

This variable is a log transformation of the cast experience variable

Figure 50: Cast experience histogram and QQ Plot

Figure 51: Cast experience boxplot

Central Tendency: The summary statistics (Table 31) the central tendency for cast experience was 2.8 log(films) and 2.8 log(films) for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.4, corresponds with a coefficient of variation of 14%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.36), indicated that the distribution of cast experience was approximately symmetric. The sample kurtosis (-0.72), indicated that the distribution of cast experience was platykurtic or light-tailed. The histogram and QQ plot in Figure 50 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 51, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 2.6, 3.2, and 0.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [1.7, 4.1]. Indeed, this confirmed the existence of no outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Cast Votes

This variable captured the total number of votes allocated to each cast member for a film.

Figure 52: Cast votes histogram and QQ Plot

Figure 53: Cast votes boxplot

Central Tendency: The summary statistics (Table 32) the central tendency for cast votes was 78,379.2 votes and 158,644.9 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 198,107.89, corresponds with a coefficient of variation of 124.9%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (2.17), indicated that the distribution of cast votes was right-skewed. The sample kurtosis (6.57), indicated that the distribution of cast votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 52 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 53, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 18,552.5, 228,174.2, and 209,621.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 542,606.75]. Indeed, this confirmed the existence of 26 outliers.

Log Cast Votes

This is a log transformation of the cast votes variable.

Figure 54: Log cast votes histogram and QQ Plot

Figure 55: Log cast votes boxplot

Central Tendency: The summary statistics (Table 33) the central tendency for log cast votes was 16.3 log(votes) and 15.9 log(votes) for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.46, corresponds with a coefficient of variation of 15.5%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.67), indicated that the distribution of log cast votes was left-skewed. The sample kurtosis (-0.08), indicated that the distribution of log cast votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 54 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 55, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 14.2, 17.8, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [8.8, 23.2]. Indeed, this confirmed the existence of 4 outliers.

Critics Scores

This variable captured the critics scores for each film

Figure 56: Critics score histogram and QQ Plot

Figure 57: Critics score boxplot

Central Tendency: The summary statistics (Table 34) the central tendency for critics score was 61 points and 57.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.37, corresponds with a coefficient of variation of 49.4%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.26), indicated that the distribution of critics score was approximately symmetric. The sample kurtosis (-1.17), indicated that the distribution of critics score was platykurtic or light-tailed. The histogram and QQ plot in Figure 56 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 57, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 83, and 50, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 158]. Indeed, this confirmed the existence of no outliers.

Log Director Experience

This variable was a log transformation of the director experience variable.

Figure 60: Log director experience histogram and QQ Plot

Figure 61: Log director experience boxplot

Central Tendency: The summary statistics (Table 36) the central tendency for director experience was 0 log(films) and 0.4 log(films) for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.6, corresponds with a coefficient of variation of 149.8%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (1.11), indicated that the distribution of director experience was right-skewed. The sample kurtosis (-0.09), indicated that the distribution of director experience was platykurtic or light-tailed. The histogram and QQ plot in Figure 60 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 61, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 0, 1, and 1, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 2.5]. Indeed, this confirmed the existence of no outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Number of IMDB Votes

This variable captured the number of IMDB votes cast for each film.

Figure 62: IMDB votes histogram and QQ Plot

Figure 63: IMDB votes boxplot

Central Tendency: The summary statistics (Table 37) the central tendency for imdb votes was 16,511 votes and 60,193.3 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 114,459.75, corresponds with a coefficient of variation of 190.2%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (3.96), indicated that the distribution of imdb votes was right-skewed. The sample kurtosis (19.12), indicated that the distribution of imdb votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 62 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 63, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5,035, 62,773, and 57,738, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 149,380]. Indeed, this confirmed the existence of 67 outliers.

Log Number of IMDB Votes

This was a log transformation of the IMDB votes variable.

Figure 64: Log IMDB votes histogram and QQ Plot

Figure 65: Log IMDB votes boxplot

Central Tendency: The summary statistics (Table 38) the central tendency for imdb log votes was 14 log votes and 14.1 log votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.35, corresponds with a coefficient of variation of 16.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.03), indicated that the distribution of imdb log votes was approximately symmetric. The sample kurtosis (-0.56), indicated that the distribution of imdb log votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 64 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 65, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 12.3, 15.9, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.9, 21.3]. Indeed, this confirmed the existence of no outliers.

IMDB Ratings

This variable captured the IMDB rating for each film

Figure 66: IMDB rating histogram and QQ Plot

Figure 67: IMDB rating boxplot

Central Tendency: The summary statistics (Table 39) the central tendency for imdb rating was 6.6 points and 6.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 1.08, corresponds with a coefficient of variation of 16.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.89), indicated that the distribution of imdb rating was left-skewed. The sample kurtosis (1.31), indicated that the distribution of imdb rating was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 66 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 67, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5.9, 7.3, and 1.4, respectively. This yielded a 1.5xIQR ‘acceptable’ range [3.8, 9.4]. Indeed, this confirmed the existence of 18 outliers.

Runtime

This is an analysis of moving runtimes.

Figure 68: Runtime histogram and QQ Plot

Figure 69: Runtime boxplot

Central Tendency: The summary statistics (Table 40) the central tendency for runtime was 103 minutes and 106.6 minutes for the median and mean, respectively.

Dispersion: The standard deviation, s = 19.12, corresponds with a coefficient of variation of 17.9%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (1.98), indicated that the distribution of runtime was right-skewed. The sample kurtosis (9.67), indicated that the distribution of runtime was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 68 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 69, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 93, 116, and 23, respectively. This yielded a 1.5xIQR ‘acceptable’ range [58.5, 150.5]. Indeed, this confirmed the existence of 16 outliers.

Log Runtime

This is an analysis of the log of moving runtimes.

Figure 70: Log runtime histogram and QQ Plot

Figure 71: Log runtime boxplot

Central Tendency: The summary statistics (Table 41) the central tendency for log runtime was 6.7 minutes and 6.7 minutes for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.24, corresponds with a coefficient of variation of 3.5%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.86), indicated that the distribution of log runtime was right-skewed. The sample kurtosis (2.06), indicated that the distribution of log runtime was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 70 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 71, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 6.5, 6.9, and 0.3, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.05, 7.35]. Indeed, this confirmed the existence of 9 outliers.

Scores

This variable captured the total score for each film defined as 10 * IMDB Rating + critics score + audience_score.

Figure 72: Scores histogram and QQ Plot

Figure 73: Scores boxplot

Central Tendency: The summary statistics (Table 42) the central tendency for total scores was 187 points and 184.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 54.52, corresponds with a coefficient of variation of 29.6%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.32), indicated that the distribution of total scores was approximately symmetric. The sample kurtosis (-0.82), indicated that the distribution of total scores was platykurtic or light-tailed. The histogram and QQ plot in Figure 72 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 73, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 145, 232, and 87, respectively. This yielded a 1.5xIQR ‘acceptable’ range [14.5, 362.5]. Indeed, this confirmed the existence of no outliers.

Log Scores

This is a log transformation of scores variable.

Figure 74: Log scores histogram and QQ Plot

Figure 75: Log scores boxplot

Central Tendency: The summary statistics (Table 43) the central tendency for log total scores was 7.5 points and 7.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.5, corresponds with a coefficient of variation of 6.7%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-1.07), indicated that the distribution of log total scores was left-skewed. The sample kurtosis (1.12), indicated that the distribution of log total scores was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 74 reveals a left skewed distribution that departs rather significantly from normality.

Outliers: The boxplot in Figure 75, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 7.2, 7.9, and 0.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.15, 8.95]. Indeed, this confirmed the existence of 13 outliers.

Theatre Days

This variable captured the number of days between theatrical and dvd release

Figure 76: Theatre days histogram and QQ Plot

Figure 77: Theatre days boxplot

Central Tendency: The summary statistics (Table 44) the central tendency for days in theatre was 391 days and 2,304.5 days for the median and mean, respectively.

Dispersion: The standard deviation, s = 3,118.24, corresponds with a coefficient of variation of 135.3%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (1.34), indicated that the distribution of days in theatre was right-skewed. The sample kurtosis (0.62), indicated that the distribution of days in theatre was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 76 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 77, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 132, 3,910, and 3,778, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 9,577]. Indeed, this confirmed the existence of 28 outliers.

Theatre Days

This variable captured the number of days between theatrical and dvd release

Figure 78: Log number of theatre days histogram and QQ Plot

Figure 79: Log number of theatre days boxplot

Central Tendency: The summary statistics (Table 45) the central tendency for days in theatre was 8.6 days and 9.3 days for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.53, corresponds with a coefficient of variation of 27.2%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (0.18), indicated that the distribution of days in theatre was approximately symmetric. The sample kurtosis (-1.16), indicated that the distribution of days in theatre was platykurtic or light-tailed. The histogram and QQ plot in Figure 78 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 79, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 7, 11.9, and 4.9, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 19.25]. Indeed, this confirmed the existence of no outliers.